00:01
In this problem, we are given the counts by weapon type for females murdered by men in a given year.
00:06
We are also given the breakdown by percent for a weapon used in all murders for that year, and we are asked if there is evidence to suggest the weapons used against women are different from the weapons used for murders in the population in general.
00:20
Here, a no hypothesis can be that the distribution of weapon type and violence against women is the same as for the whole population.
00:29
So let's write that down.
00:54
And the alternative hypothesis then would be that the distribution of weapon type is different for women than it is for the general population.
01:04
So in this case, our model distribution is the weapon distribution for the overall population.
01:10
And we are testing whether the weapon distribution against women is a good fit for that model.
01:15
So this is a goodness of fit test.
01:18
So first let's check the necessary conditions.
01:21
So one is counted data.
01:28
And indeed we do have counted data.
01:33
So the counts by weapon type for women's murders are there.
01:38
So that's good.
01:41
Number two is independence assumption and randomization.
02:04
So we do not expect that one woman's murder will have an influence on the weapon used for another.
02:10
This could be the case for serial killings in which the murder has a preferred weapon, but most murders are not performed by serial killers.
02:19
And with respect to randomization, all things.
02:22
Although this is not a random sample, it is an exhaustive sample for that year.
02:26
So we can take these murders to be representative of all women murdered in general.
02:32
So we are good here...